Research Article

Exponential Operators For Generalized Lamb–Bateman Singular Integral Equations

Volume: 5 Number: 2 October 30, 2017
EN

Exponential Operators For Generalized Lamb–Bateman Singular Integral Equations

Abstract

In this article, the author extends the application of exponential operators to solve certain non-linear fractional differential equation, space fractional partial differential equation and two dimensional Lamb– Bateman singular integral equation. Numerous constructive examples and exercises presented throughout the paper. The main purpose of this work is to present mathematical results that are useful to researchers in a variety of fields.

Keywords

Laplace transforms,Caputo fractional derivative,Parabolic Cylinder function,Riemann-Liouville fractional derivative,Lamb- Bateman singular integral equation

References

  1. [1] Aghili, A., New results involving Airy polynomials, fractional calculus and solution to generalized heat equation, New trends in mathematical sciences, 3 (2015).
  2. [2] Aghili, A., Fractional Black–Scholes equation, International Journal of Financial Engineering, 4 (1) (2017) World Scientific Publishing Company, DOI: 10.1142/S2424786317500049.
  3. [3] Apelblat, A., Laplace transforms and their applications, Nova Science Publishers Inc., New York, 2012.
  4. [4] Babusci, D., Dattoli, G., Sacchetti, D., The Lamb-–Bateman Integral Equation and the Fractional Derivatives, Fractional calculus and applied analysis, 14 (2) (2011), 317–320.
  5. [5] Dattoli, G., Operational methods, fractional operators and special polynomials. Applied Mathematics and Computations, 141 (2003) 151–159.
  6. [6] Dattoli, G., Srivastava, H.M., Zhukovsky, K.V., Operational methods and differential equations to initial value problems. Applied Mathematics and computations, 184 (2007) 979–1001.
APA
Aghili, A. (2017). Exponential Operators For Generalized Lamb–Bateman Singular Integral Equations. Mathematical Sciences and Applications E-Notes, 5(2), 1-9. https://doi.org/10.36753/mathenot.421723
AMA
1.Aghili A. Exponential Operators For Generalized Lamb–Bateman Singular Integral Equations. Math. Sci. Appl. E-Notes. 2017;5(2):1-9. doi:10.36753/mathenot.421723
Chicago
Aghili, Arman. 2017. “Exponential Operators For Generalized Lamb–Bateman Singular Integral Equations”. Mathematical Sciences and Applications E-Notes 5 (2): 1-9. https://doi.org/10.36753/mathenot.421723.
EndNote
Aghili A (October 1, 2017) Exponential Operators For Generalized Lamb–Bateman Singular Integral Equations. Mathematical Sciences and Applications E-Notes 5 2 1–9.
IEEE
[1]A. Aghili, “Exponential Operators For Generalized Lamb–Bateman Singular Integral Equations”, Math. Sci. Appl. E-Notes, vol. 5, no. 2, pp. 1–9, Oct. 2017, doi: 10.36753/mathenot.421723.
ISNAD
Aghili, Arman. “Exponential Operators For Generalized Lamb–Bateman Singular Integral Equations”. Mathematical Sciences and Applications E-Notes 5/2 (October 1, 2017): 1-9. https://doi.org/10.36753/mathenot.421723.
JAMA
1.Aghili A. Exponential Operators For Generalized Lamb–Bateman Singular Integral Equations. Math. Sci. Appl. E-Notes. 2017;5:1–9.
MLA
Aghili, Arman. “Exponential Operators For Generalized Lamb–Bateman Singular Integral Equations”. Mathematical Sciences and Applications E-Notes, vol. 5, no. 2, Oct. 2017, pp. 1-9, doi:10.36753/mathenot.421723.
Vancouver
1.Arman Aghili. Exponential Operators For Generalized Lamb–Bateman Singular Integral Equations. Math. Sci. Appl. E-Notes. 2017 Oct. 1;5(2):1-9. doi:10.36753/mathenot.421723